It basically means that it's thickness is infinitesimal. You still see it, but e.g. if you zoom in with a transformation, it won't get thicker. At the same time, it won't disappear if you zoom out either. It's in some sense the smallest thing the device can draw to represent the mathematical line segment.

Elias

As a side effect, hairlines are undefined to as in which pixels are lit up. If you specify a thickness, the GPU guarantees that each pixel whose center lies inside of the line is lit. If you draw a hairline, the GPU is pretty much free to do whatever it wants.